From my trip in March, 2012, here are a couple of suggestions for remote areas where you might enjoy boondocking.
Las Cienegas National Conservation Area Camping info on the webpage.
Buenos Aires National Wildlife Refuge There are designated remote sites, I think about 100 of them! Amazing place.
I also stayed some state and USFS campgrounds (Catalina, Patagonia Lake, Madera Canyon, Organ Pipe), but those might be too tame for your tastes.
Do remember that the border is nearby. You may not want your camp to be viewed as a supply depot for illegal border crossers. I saw several of them, plus many Border Patrol vehicles.
Here are a few photos from my trip:
https://picasaweb.google.com/CVKSmith/ExploringSouthernAZMarch2012